Low temperature thermodynamics of inverse square spin models in one dimension

TL;DR

This paper uses a field-theoretic renormalization group approach to analyze the low-temperature thermodynamics of inverse square spin models in one dimension, revealing a specific divergence in magnetic susceptibility.

Contribution

It provides a two-loop order calculation for classical O(N)-models with inverse square interactions near their lower critical dimension, linking classical and quantum models.

Findings

Magnetic susceptibility diverges as T^{-a} exp(b/T) at low temperatures.

The temperature dependence matches that of the exactly solvable Haldane-Shastry model.

Results apply to both classical and quantum ferromagnetic spin chains.

Abstract

We present a field-theoretic renormalization group calculation in two loop order for classical O(N)-models with an inverse square interaction in the vicinity of their lower critical dimensionality one. The magnetic susceptibility at low temperatures is shown to diverge like $T^{-a} \exp(b/T)$ with $a=(N-2)/(N-1)$ and $b=2\pi^2/(N-1)$. From a comparison with the exactly solvable Haldane-Shastry model we find that the same temperature dependence applies also to ferromagnetic quantum spin chains.